Question

На тренировке лыжник пробежал первый круг на 5% быстрее,чем второй,а третий круг- на 14% медленнее,чем во второй.Сколько времени в среднем он тратил на один круг,если третий круг он пробежал на 4 мин 45 сек медленнее чем первый?На сколько процентов времени он затратил на прохождение третьего круга,чем первого?

Answer 1

Первый круг 100% или 1
второй круг 105% или 1,05
третий 119% или 1,19
получим что 4 мин 45 сек или 4,75 мин это 19% или 0,19
найдем 100%:4,75/19*100=25 мин - 1й круг
25*1,05=26,25 мин - 2й круг
25*1,19=29,75 мин - 3й круг
(25+26,25+29,75)/3=27 мин в среднем тратил на прохождение одного круга
на третий круг затрачено на 19% времени больше чем на первый

Answer 2

Calculation of Average Time per Lap

To calculate the average time per lap, we need to determine the time taken for each lap and then find the average of those times.

Let's assume the time taken for the first lap is x minutes. According to the given information, the second lap was completed 5% faster than the first lap. Therefore, the time taken for the second lap would be 0.95x minutes.

Similarly, the third lap was completed 14% slower than the second lap. So, the time taken for the third lap would be 1.14(0.95x) minutes.

Given that the third lap was completed 4 minutes and 45 seconds slower than the first lap, we can set up the following equation:

x + 4 minutes 45 seconds = 1.14(0.95x) minutes

To solve this equation, we need to convert 4 minutes 45 seconds to decimal form. Since 1 minute is equal to 60 seconds, 4 minutes 45 seconds is equal to 4.75 minutes.

Now, let's solve the equation:

x + 4.75 = 1.14(0.95x)

Simplifying the equation:

x + 4.75 = 1.083x

4.75 = 0.083x

Dividing both sides by 0.083:

x ≈ 57.23 minutes

Therefore, the time taken for the first lap is approximately 57.23 minutes.

To find the average time per lap, we need to calculate the sum of the times for all three laps and divide it by the number of laps (which is 3):

Average time per lap = (x + 0.95x + 1.14(0.95x)) / 3

Substituting the value of x:

Average time per lap = (57.23 + 0.95 * 57.23 + 1.14 * 0.95 * 57.23) / 3

Calculating the average time per lap:

Average time per lap ≈ 57.23 minutes

Therefore, the average time per lap is approximately 57.23 minutes.

Percentage Difference Between the Third and First Laps

To calculate the percentage difference between the time taken for the third lap and the time taken for the first lap, we can use the following formula:

Percentage difference = ((Third lap time - First lap time) / First lap time) * 100

Substituting the values:

Percentage difference = ((4 minutes 45 seconds) / (57.23 minutes)) * 100

Converting 4 minutes 45 seconds to decimal form:

Percentage difference = (4.75 minutes / 57.23 minutes) * 100

Calculating the percentage difference:

Percentage difference ≈ 8.29%

Therefore, the athlete spent approximately 8.29% more time on the third lap compared to the first lap.